Question about cover. I'm not sure if the rules specify and I can't find it, or if someone has good suggestions. To explain what I'm asking, I'll use the map below. The line of Ys between D column and E column is a wall. The "D" between D3 and E3 is a doorway. There are three characters (EF, DR, and NE). If EF is standing on one side of the doorway and NE is standing on the other side of the doorway so that NE is diagonal to EF with the doorframe between them, how much cover is appropriate? Half cover? Three quarters cover?

The obstacle for half-cover "might be a low wall, a large piece of furniture, a narrow tree trunk, or a creature". The obstacle for 3/4 cover "might be a portcullis, an arrow slit, or a thick tree trunk".

For me, that obstacle isn't quite the level of an arrow slit, and is closer to a narrow tree trunk, so I'd call it half-cover.

I concur with TheGreyWulf on this one; due to the angle of positioning, the door frame would provide roughly half cover (though I would allow it to be considered 3/4 cover if the character were also fighting defensively). In order to react or attack effectively across the span of a doorway, roughly half of one's body would need to be exposed, particularly if the character is using anything the size of a longsword or greater. This argument might change if you're playing a more modern setting where gun combat is prominent; you could fight across a doorway using a pistol or a one-handed weapon and treat it as 3/4 cover, but a rifle or other two-handed weapon would make it half.

It’s 5e, so this is very much the sort of thing left up to the individual GM to rule on in particular situations.

But I agree with the previous two respondents, and I think TheGreyWulf has laid it out nicely: this seems more like half-cover if you compare it to the sort of thing that is given in the examples. The intent is clearly that three-quarters cover = very little of the target is visible, even when they expose themselves to attack you.

Worth remembering that an “attack” is an abstraction for a whole bunch of things going on simultaneously, including maneuvering for position by both parties.